Related papers: Counterexamples to the Low-Degree Conjecture
Two-sample hypothesis testing for network comparison presents many significant challenges, including: leveraging repeated network observations and known node registration, but without requiring them to operate; relaxing strong structural…
In algorithmic randomness, when one wants to define a randomness notion with respect to some non-computable measure $\lambda $, a choice needs to be made. One approach is to allow randomness tests to access the measure $\lambda $ as an…
An elegant characterization of the complexity of constraint satisfaction problems has emerged in the form of the the algebraic dichotomy conjecture of [BKJ00]. Roughly speaking, the characterization asserts that a CSP {\Lambda} is tractable…
A low-degree test is a collection of simple, local rules for checking the proximity of an arbitrary function to a low-degree polynomial. Each rule depends on the function's values at a small number of places. If a function satisfies many…
Higher-order tensor methods were recently proposed for minimizing smooth convex and nonconvex functions. Higher-order algorithms accelerate the convergence of the classical first-order methods thanks to the higher-order derivatives used in…
While statistics and machine learning offers numerous methods for ensuring generalization, these methods often fail in the presence of adaptivity---the common practice in which the choice of analysis depends on previous interactions with…
In supervised learning, automatically assessing the quality of the labels before any learning takes place remains an open research question. In certain particular cases, hypothesis testing procedures have been proposed to assess whether a…
To model modern large-scale datasets, we need efficient algorithms to infer a set of $P$ unknown model parameters from $N$ noisy measurements. What are fundamental limits on the accuracy of parameter inference, given finite signal-to-noise…
The identification of new rare signals in data, the detection of a sudden change in a trend, and the selection of competing models, are among the most challenging problems in statistical practice. These challenges can be tackled using a…
This paper studies hypothesis testing and parameter estimation in the context of the divide and conquer algorithm. In a unified likelihood based framework, we propose new test statistics and point estimators obtained by aggregating various…
Although the standard formulations of prediction problems involve fully-observed and noiseless data drawn in an i.i.d. manner, many applications involve noisy and/or missing data, possibly involving dependence, as well. We study these…
In this paper, we investigate the relative power of several conjectures that attracted recently lot of interest. We establish a connection between the Network Coding Conjecture (NCC) of Li and Li and several data structure like problems…
Motivated by the search for a counterexample to the Poincar\'e conjecture in three and four dimensions, the Andrews-Curtis conjecture was proposed in 1965. It is now generally suspected that the Andrews-Curtis conjecture is false, but small…
The bootstrap is a popular data-driven method to quantify statistical uncertainty, but for modern high-dimensional problems, it could suffer from huge computational costs due to the need to repeatedly generate resamples and refit models. We…
The Sum-of-Squares (SoS) hierarchy, also known as Lasserre hierarchy, has emerged as a promising tool in optimization. However, it remains unclear whether fixed-degree SoS proofs can be automated [O'Donnell (2017)]. Indeed, there are…
This paper is an attempt to set a justification for making use of some dicrepancy indexes, starting from the classical Maximum Likelihood definition, and adapting the corresponding basic principle of inference to situations where…
Stochastic gradient descent is one of the most common iterative algorithms used in machine learning and its convergence analysis is a rich area of research. Understanding its convergence properties can help inform what modifications of it…
In the number partitioning problem (NPP) one aims to partition a given set of $N$ real numbers into two subsets with approximately equal sum. The NPP is a well-studied optimization problem and is famous for possessing a…
Researchers often misinterpret and misrepresent statistical outputs. This abuse has led to a large literature on modification or replacement of testing thresholds and $P$-values with confidence intervals, Bayes factors, and other devices.…
Many natural combinatorial problems can be expressed as constraint satisfaction problems. This class of problems is known to be NP-complete in general, but certain restrictions on the form of the constraints can ensure tractability. The…